Dependence on choices Sample Clauses

Dependence on choices. In this subsection we will give the definition of an admissible set which gives a numerical criterion on a subset of basis elements ci,j for their span to be independent of choices. Later we will use this criterion to find explicit formulae. This subsection is a direct generalisation of §6 of [DDR16]. p Our set-up is the same as in the previous subsection. Let p > 2 be an odd prime. Suppose K/Qp is a finite extension of ramification index e, of residue degree f and with residue field k. Moreover, we take χ : GK → Fˆ to be any continuous character. Let M = L(π) be a totally tamely ramified extension of an unramified extension L/K of degree prime-to-p, where the ramification degree eM of M /K satisfies eM | pf — 1, the uniformiser π of M M satisfies πeM < Kˆ and we take M sufficiently large so that χ|G is trivial.
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Related to Dependence on choices

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